Systems and methods for trading actively managed funds

ABSTRACT

The invention provides systems and methods for intra-day trading of actively managed exchange traded funds (AMETFs). The invention provides creation and redemption structures for AMETF shares that allow arbitrage, intra-day value estimations for AMETF shares, and hedging portfolios for hedging risks associated with trading AMETF shares, all without requiring disclosure of the specific assets underlying the AMETF.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of pending U.S. patent application Ser.No. 10/753,069, filed Jan. 8, 2004; U.S. Ser. No. 09/536,663, filed Mar.27, 2000 (U.S. Pat. No. 6,941,280, issued Sep. 6, 2005); Ser. No.09/536,258, filed on May 27, 2000 (U.S. Pat. No. 7,099,838, issued Aug.29, 2006); Ser. No. 09/815,589, filed on May 23, 2001; Ser. No.10/123,779, filed on Apr. 16, 2002 (U.S. Pat. No. 7,305,362), withpriority to British patent application Serial No. 0206440.0, filed onMar. 18, 2002; and Ser. No. 10/174,505, filed on Jun. 17, 2002.

FIELD OF THE INVENTION

This invention relates to systems and methods to allow public intra-daytrading of financial instruments such as shares of actively managedfunds on secondary markets without knowledge of the specific assetsunderlying the traded instruments.

BACKGROUND

Mutual funds allow investors to trade in a variety of assets in a singleinvestment vehicle. For example, a mutual fund may comprise shares ofstocks of many different companies. Mutual funds may also be comprisedof one or more types of financial instruments—stocks, bonds, options,futures, etc.—and may involve securities from diverse industries. Mutualfunds provide the benefit of investment diversification withoutrequiring investment expertise or extensive knowledge about theunderlying assets. Furthermore, investors can benefit from professionalexperience when they hold actively managed funds (“AMFs”), in whichexpert fund managers apply their knowledge of markets to select assetsto buy for and sell from the funds they manage.

Managers of AMFs keep secret their day to day trading of fund assets andthe identities and quantities of the underlying assets (portfolios) ofthe funds they manage. Fund secrecy prevents others from “freeriding”—benefiting from managers' expert knowledge without investing intheir funds and without paying fund management fees. Secrecy alsoprevents “front running”—observing fund trading trends to benefit fromincreasing or decreasing stock prices resulting from the fund'sacquiring or selling off shares of the stock. While periodic reportingof fund assets is required, the reporting periods are long enough (e.g.,quarterly or semi-annually with a 45 day lag) to prevent informationabout the AMF holdings to be sufficiently current to enable free ridingor front running.

Current market regulations do not allow intra-day market trading ofAMFs. Instead, investor orders to buy or sell AMFs received during theday are processed after market close, with the price based on the netasset value (“NAV”) of the fund. The NAV is conventionally calculatedfor the current trading day after market close based on the assets heldin the fund at the close of the previous trading day and the value ofthose assets at the close of the current trading day. One difficultywith implementing a system for intra-day market trading of AMFs is thatinvestors have insufficient information on which to base negotiatedtrading prices because they currently have no way of knowing either thespecific assets in the AMF portfolio or their NAV.

Another difficulty with implementing a system for intra-day markettrading of AMFs is that many market participants, and especially marketspecialists and market makers, who match buy orders with sell orders orbuy and sell stocks themselves to keep markets orderly and liquid, mustbe able to hedge their trading risks. Throughout this application,market makers, market specialists, and any other market liquidityproviders will be referred to as “liquidity providers.” When liquidityproviders receive more orders to sell a stock than to buy it, they maybuy the stock themselves and wait for more buy orders for that stock.Meanwhile, they risk the possibility that the value of the stock theyhold will fall while they are holding it. They may hedge against thisrisk by making some trade that offsets the risk. But if the orders wereto involve AMFs, then the liquidity providers would lack knowledge ofthe underlying assets, and thus would lack sufficient information to beable to effectively hedge this risk. Their inability to effectivelyhedge would result in an unacceptably wide spread between bid and offerprices, which in turn would inhibit trading.

In 1993, the American Stock Exchange (“AMEX”) introduced a class offunds that can be traded intra-day on public stock exchanges. Theseexchange-traded finds (“ETFs”) are generally based on some recognizedindex and thus have publicly known and published holdings. Like AMFs,ETFs provided investors with convenient diversification, but they alsoprovided convenient trading platforms in secondary markets such as stockexchanges. For example, ETF index funds consist mostly of shares of thestocks in the same proportion as those used to calculate stock marketindices, and have market values that vary with those indices. Well-knownexchange traded funds include the SPDR Trust (“SPY”), which tracks theS&P 500 Index, the Nasdaq 100 Trust (“QQQ”), which tracks the Nasdaq 100Index, and the Diamonds Trust (“DIA”), which tracks the Dow JonesIndustrial Average. Information sufficient to accurately estimate thecompositions of these finds is publicly available on a day-to-day andintra-day basis, and estimates of the intra-day values of these findscan be computed during intra-day trading based on the intra-day valuesof their underlying assets at the start of the trading day. Marketliquidity providers can hedge in situations in which there is a shortterm oversupply or over-demand of these funds because they know exactlywhich stocks comprise the funds. Current ETFs may be considered“passively managed” funds, because the fund managers do not useforecasting expertise to decide investment strategies, but rather simplymaintain portfolios that reflect the compositions of the indices theyare intended to track.

The AMEX obtained exemptions from certain securities regulations thatallow its ETFs to function successfully while maintaining fairinvestment practices. One such exemption allows intra-day trading ofETFs by allowing trading at negotiated prices rather than the NAV of theunderlying assets. Another exemption encourages trading of ETFs onsecondary markets by allowing the fund company to issue and redeem ETFshares only in large aggregations called “creation units” of manythousands of ETF shares. Creation units are purchased with “portfoliodeposits” equal in value to the NAV of the ETF shares in the creationunits. The compositions of portfolio deposits are published by ETF fundmanagers daily, and usually reflect the proportionate assets in the ETFportfolio. Investors must redeem ETF shares only in creation unitaggregations. The fund presents an investor redeeming a creation unitwith a “redemption basket.” The compositions of redemption baskets arealso published by ETF managers daily, and also usually reflect theproportionate assets in the ETF portfolio. After a creation unit ispurchased, the ETF shares can be traded individually on secondarymarkets, but individual ETF shares may not be redeemed with the fundcompany itself.

The securities regulations exemptions enjoyed by ETFs are justifiedbecause the transparent, open-ended creation/redemption structure allowsnegotiated prices of ETF shares on secondary markets to be keptsubstantially in line with the intra-day value of the underlying assetsby arbitrage. If the price of ETF shares is significantly less than thevalue of the underlying securities, then arbitragers can purchase enoughETF shares to assemble a creation unit, redeem the creation unit withthe fund for a redemption basket, and simultaneously sell the underlyingsecurities in the redemption basket (or futures contracts representingthe underlying securities), thus realizing a profit. This additionaldemand for ETF shares tends to bring their price up to the intra-dayvalue. If the price of ETF shares is significantly greater than theintra-day value, on the other hand, then arbitragers can purchase theunderlying securities to assemble a portfolio deposit and purchase acreation unit, and simultaneously sell the ETF shares on the secondarymarkets at a profit. The additional supply of ETF shares tends to bringtheir price down to the intra-day value. The substantial equivalence ofETF share prices in transactions with the fund company and on secondarymarkets resulting from arbitrage ensures that larger institutionalinvestors are not favored over smaller individual investors.

Investors have embraced many ETFs for their convenient diversificationin a single investment instrument and the trading flexibility theyallow. Because of the success of current ETFs, there has beensignificant interest in allowing more management freedom than iscurrently possible in ETFs. But part of the value of any activelymanaged fund is in portfolio secrecy, which obstructs pricing evaluation(because the intra-day value is unknown), hedging (because the portfoliois unknown), and arbitrage (because to preserve portfolio secrecy,creation/redemption baskets may not be representative of the fundholdings). There is, therefore, a need for systems and methods to allowintra-day trading of AMFs by providing a creation/redemption structurethat promotes arbitrage and providing information equivalent to theintra-day values and portfolios of AMFs without disclosure of thespecific assets of the funds.

SUMMARY

The invention includes methods of using computer means to select asecond set of securities that substantially tracks the returns of afirst set of securities over the course of a trading day, wherein thesecond set of securities serves as a proxy for the first set ofsecurities, and market participants use the second set of securities toprice or hedge a position taken in the first set of securities withoutknowing the composition of the first set of securities. Any mathematicalmethod may be used to select the second set of securities including, forexample, economic or statistical risk factor models or Monte Carlomethods. The invention further includes systems for performing thesemethods.

One embodiment of the invention includes a method for permittingefficient trading of shares of a fund without revealing the fund assets,comprising: determining a set of risk factors from a risk factor model,receiving or calculating a set of fund sensitivity coefficients andstoring the set of fund sensitivity coefficients on computer readablemedia, wherein each fund sensitivity coefficient specifies the exposureof the fund to one of the risk factors, and using computer means tocreate a proxy portfolio having substantially the same sensitivitycoefficients as the fund. Another embodiment further includes the stepsof calculating an estimated value for the fund based on the value of theproxy portfolio, wherein the step of calculating the estimated value isrepeated periodically throughout a trading period, and publishing theestimated value periodically throughout the trading period. Anotherembodiment additionally or alternatively includes the step of creating ahedging portfolio, wherein the hedging portfolio has substantially thesame sensitivity coefficients as the fund.

The risk factor model may be an economic risk factor model, and the riskfactors may include unexpected changes in default premiums, unexpectedinterest rate changes, unexpected changes in inflation rates, unexpectedchanges in long term economic growth, market risk as measured by abenchmark index, unexpected changes in debt term structure, riskpremium, firm size effects, leverage, and/or book-to-market equity.

Alternatively, the risk factor model may be a statistical risk factormodel, such as principal components analysis. In this embodiment, themethod may further comprise the step of selecting securities for a proxyuniverse, wherein the step of creating a proxy portfolio involvescalculating weights of securities in the proxy universe. The riskfactors may be calculated by orthogonalizing a correlation matrix ofreturns functions of the securities in the proxy universe. The step ofmeasuring the exposure of the fund to the set of risk factors mayinclude a linear least squares regression.

In one embodiment, the method may further comprise the steps of sortingthe securities in the proxy universe into a plurality of groups,creating a correlation matrix of returns functions of the securities ineach group of securities, thereby creating a correlation matrix for eachgroup, orthogonalizing the correlation matrix for each group to producea first set of eigenvalues and corresponding eigenvectors for eachgroup, arranging the first set of eigenvalues for each group indescending order, eliminating a number of the smallest eigenvalues fromthe first set of eigenvalues and their corresponding eigenvectors fromeach group according to predetermined elimination criteria to produce areduced set of principal components for each group, creating acorrelation matrix between all of the principal components in thereduced set of principal components for each group, orthogonalizing thecorrelation matrix between all of the principal components in thereduced set of principal components for each group to produce a secondset of eigenvalues and corresponding eigenvectors for all reducedgroups, and eliminating a number of the smallest eigenvalues and theircorresponding eigenvectors from the second set of eigenvalues andcorresponding eigenvectors to produce a set of risk factors.

An embodiment of the invention includes a method for creating a proxyportfolio for a fund without revealing the fund assets, comprising thesteps of: measuring an exposure of the fund to a set of risk factors toproduce a set of fund sensitivity coefficients, wherein the risk factorscomprise a historical time series of price data for a set of securitiesand each fund sensitivity coefficient indicates the exposure of the fundto one of the risk factors, storing the fund sensitivity coefficients oncomputer readable media; and using computer means to create a proxyportfolio from securities selected from a proxy universe of securities,wherein the proxy portfolio has substantially the same sensitivitycoefficients as the fund.

An embodiment of the invention includes a method for creating a hedgingportfolio for a fund without revealing the fund assets, comprising thesteps of measuring an exposure of the fund to a set of risk factors toproduce a set of fund sensitivity coefficients, wherein the risk factorscomprise a historical time series of price data for a set of securitiesand each fund sensitivity coefficient indicates the exposure of the fundto one of the risk factors; storing the fund sensitivity coefficients oncomputer readable media; using computer means to create a proxyportfolio from securities selected from a proxy universe of securities,wherein the proxy portfolio has substantially the same sensitivitycoefficients as the fund; and using computer means to create a hedgingportfolio based on the proxy portfolio.

An embodiment of the invention includes a method for creating a reducedrisk hedging portfolio for a fund without revealing the fund assets,comprising the steps of measuring an exposure of the fund to a pluralityof risk factors to produce a set of fund sensitivity coefficients,wherein the risk factors comprise a historical time series of price datafor a set of securities in the hedging portfolio; storing the fundsensitivity coefficients on computer readable media; using computermeans to determine the exposure of each of the securities in a hedginguniverse of securities to the risk factors; and using computer meansprogrammed with risk minimizer software to produce a reduced riskhedging portfolio.

In other embodiments, the invention includes systems for performing themethods described above, including computer means for performing any orall of the steps of the methods described above. The systems of theinvention may include a computer programmed with a graphical userinterface, including a graphical dial, slide bar, or other graphicalindicator for adjusting user inputs, wherein the user inputs areselected from the group consisting of the size of aggregation buckets,database minimum data density requirements, banding time, the number ofreturns used to build the model, the type of weighting, the percentvariation used for eigenvalue and factor culling, and the total numberof factors to be used in the model. In still other embodiments, theinvention includes data storage devices storing software instructions tocause a computer to perform the methods described above.

DESCRIPTIONS OF THE FIGURES

FIG. 1 is a process of the invention for providing an intra-day value ofan AMETF involving encryption, decryption, and an intra-day valuecalculation based on the AMETF.

FIG. 2 is a process of the invention for providing an intra-day value ofan AMETF.

FIG. 3 is a process of the invention for providing an intra-day valueproxy and a hedging portfolio for use in trading an AMETF based on afactor model of the AMETF that need not involve disclosure of the assetsunderlying the AMETF.

FIG. 4 is an embodiment of the process shown in FIG. 3, where the factormodel is an economic factor model.

FIG. 5 is an embodiment of the process shown in FIG. 3, where the factormodel is a statistical factor model.

FIG. 5A outlines the steps of the basic PCA process for finding riskfactors for use in building a statistical factor model.

FIG. 5B outlines the steps of a two-step PCA process for finding riskfactors for use in building a statistical factor model.

FIG. 6 is an embodiment of a process for constructing an optimizedhedging portfolio with minimum deviation from a proxy portfolio.

FIG. 7 is a histogram of the percent differences in intra-day valuesbetween a proxy portfolio model created according to the methods of theinvention and the AMETF that the proxy portfolio models for eachreporting period (every 10 minutes) for each trading day in an entireyear.

FIG. 8 is a graph illustrating that a proxy portfolio constructedaccording to the methods of the invention accurately tracks the AMETFportfolio it models throughout a trading day.

FIG. 9 is a graph illustrating that an optimized hedging portfolioconstructed according to the methods of the invention accurately tracksthe AMETF portfolio.

DETAILED DESCRIPTION

The invention provides systems and methods that allow trading of anyfund while maintaining secrecy of the specific assets of the fund. Whilemuch of the following description is in terms of AMETFs, the fundstraded using the systems and methods of the invention can include (andthe term “fund” as used herein includes at least the following): anytype of investment instrument including, for example, shares of mutualfunds, unit investment trusts (UITs), closed-end funds, grantor trusts,hedge funds, any investment company, or any other type of collectiveinvestment. Furthermore, while the examples provided herein demonstrateintra-day trading of fund shares on a stock exchange without disclosureof fund assets, the systems and methods of the invention are equallyapplicable to trading of secret-asset fund shares at any time on anyvenue, market, or exchange, for example, after hours trading on a U.S.or foreign exchange, or on an electronic trading network (ECN) orover-the-counter, third market, or other off-exchange trading venue.

The invention provides structures for creating and redeeming AMETFshares that allow arbitrage, methods for publishing an intra-day assetvalue that can be used by investors to base negotiated prices, andportfolios that can be used by market liquidity providers and others tohedge risks from trading AMETF shares. The information provided by theinvention need not include specific information about the specific fundholdings or information sufficient even to determine approximate fundholdings. Instead, the information should be sufficient to createportfolios that mimic the behavior of AMETFs accurately enough to basenegotiated prices of the AMETFs on and to hedge AMETF investment risks.

In accordance with the invention, AMETFs may be organized as investmentcompanies (or fund companies), which are companies that issue securitiesand whose primary business is investment. In a preferred embodiment,AMETFs may be open-ended, and thus issue shares that may be redeemed bythe investment company for their NAV. While AMFs are currently nottraded on secondary markets, the structures, systems, and methodsdescribed below can allow exchange trading. While most ETFs are open-endmanagement investment companies, some ETFs are organized as UITs, and asimilar organizational structure may be used for AMETFs. In analternative embodiment, AMETFs may be organized as closed-end companies,which issue shares that are not redeemable by the fund company at alltimes, but rather are traded primarily on secondary markets.

There are a number of ways in which the distribution structure of AMETFshares may be organized. One way is to allow cash transactions with thefund company, thus allowing the purchase and redemption of AMETF sharesfor cash, as most AMFs are organized. Preferably, cash transactions withthe fund company are executed at the end of the trading day based on theNAV of the fund at market close, as with most AMFs. Alternatively, cashtransactions may be made with the fund company during the trading day.The benefits of cash transactions are that they are simple to implementand require no disclosure of the fund portfolio. However, otheralternatives are preferable for many reasons. One reason is the cashexposure risk: when fund companies sell AMETF shares for cash, the fundgains cash at the expense of a proportionate value of the fundportfolio, which negatively affects the performance of the fund if thevalue of the securities in the fund portfolio increases more than thevalue of an equivalent amount of cash. The fund manager will thus wantto convert all the cash into the securities in the fund portfolio, whichresults in transaction costs including brokerage commissions andbid/offer spread costs. Furthermore, cash transactions can causepotentially adverse tax consequences on any gains realized.

Another way in which AMETF shares may be distributed and redeemedinvolves the fund manager defining and publishing creation andredemption baskets each day, and traders purchase and redeem shares ofthe AMETF by assembling creation baskets to purchase shares andreceiving redemption baskets upon redemption of shares. This structureresembles that of ETFs, with an important difference. With ETFs, thefund portfolio is essentially public knowledge, which allows thecreation and redemption baskets to reflect the assets underlying thefund itself. But AMETF portfolios are preferably kept secret, so thecreation and redemption baskets preferably do not reflect the fund'sunderlying assets because publication of the basket portfolios wouldreveal the fund portfolios. Thus in one creation/redemption basketembodiment, AMETF fund managers may be given flexibility to select thesecurities that comprise creation and redemption baskets. Thisflexibility would allow fund managers to alter the fund compositionthrough creation and redemption according to investment strategies whilemaintaining fund secrecy by selecting baskets that need not reflect theactual fund portfolio. This structure provides the benefits of little orno cash exposure risk, minimized transaction costs for the fund, taxefficiencies, and limited disclosure of information relating to fundcomposition.

A related creation/redemption structure can involve the specification ofa “factor basket,” which is a basket not of financial instruments, butrather of information regarding the exposure of the AMETF portfolio tocertain pre-specified or unspecified factors. Several examples areprovided below of how to select factors and calculate the exposure ofAMETF portfolios to the factors. In a factor basket embodiment, anygroup of securities that has substantially the same exposure to thefactors in the factor creation basket (and the same NAV as a creationunit) can be used to buy fund shares, or any group of securities withsubstantially the same exposure to the factors in a redemption basket(with the same NAV as a creation unit) can be received in exchange forfind shares. However, it is anticipated that the arbitrageurs andinstitutional investors who would be the primary entities dealingdirectly with the find company would tend to put disfavored stocks(e.g., not actively traded) in the creation basket, if given the choice.The fund would then own the disfavored stocks, which may be difficult totrade if they are illiquid. It is likewise anticipated that the fundcompany would tend to put disfavored stocks in redemption baskets. Thesetendencies may inhibit arbitrage. One way to overcome this would be torequire traders and the fund company to select from a predetermineduniverse of instruments in order to generate creation and redemptionbaskets having substantially the same exposures to the designatedfactors as the AMETF portfolio. Such a structure provides the benefitsof minimizing cash exposure risk, tax efficiencies, and limiteddisclosure of information relating to fund composition. However, therewould be some transaction costs associated with converting thesecurities received in creation baskets into securities to be held inthe AMETF.

The preferred creation/redemption structure uses benchmark index ETFs increation and redemption baskets. For example, creation and redemptionbaskets for an AMETF may comprise SPDRs, shares in an ETF comprisingessentially the same shares of stocks of the companies in essentiallythe same proportions underlying the S&P 500 index, even though the AMETFportfolio itself may contain a different set of stocks and/or adifferent set of proportions. In another embodiment, the creation andredemption baskets may contain securities underlying one or morebenchmark indices in the same or different proportions than in thoseindices. In yet another embodiment, the creation and redemption basketsmay contain securities underlying one or more benchmark indices inproportions specified by the find manager. When the creation andredemption baskets comprise benchmark index ETFs, this minimizes cashexposure risk, limits the disclosure of information relating to theAMETF portfolio, and eliminates the benchmark risk (i.e., the risk thatthe value of the assets in the creation basket will underperform thefund's index benchmark).

In one embodiment, the invention includes methods for providing anintra-day value proxy for an AMETF without disclosure of the fund'sunderlying assets. Market rules and securities regulations require thevalues of ETFs to be published frequently throughout the day, forexample, every 15 seconds. Similarly frequent intra-day valueinformation will need to be provided for AMETFs, with a concurrent needto keep the fund portfolio secret.

FIG. 1 shows a method that can provide updated intra-day valueinformation for an AMETF throughout the day without public disclosure ofthe underlying assets. A fund computer 110 stores a portfolio file 115,that contains the identities and quantities of all of the fund holdings.The fund computer 110 preferably includes standard protections againstunauthorized access to the portfolio file (for example, passwordprotection and a firewall). The fund computer may be operated by anagent of the fund, e.g., the fund manager, administrator, or custodian.In step 120, the portfolio file may be encrypted using any knownencryption techniques and algorithms to generate an encrypted portfoliofile 125.

In step 127, the encrypted portfolio file 125 is sent to anothercomputer 130, referred to here as a pricing computer. The pricingcomputer 130 may be operated, for example, by an exchange that lists theAMETF. Alternatively, the pricing computer 130 may be operated by athird party that transmits intra-day value information to an exchange,or the pricing computer may be operated by an agent of the fund itself(see, for example, the embodiment of FIG. 2). In step 135, the pricingcomputer 130 decrypts the encrypted portfolio file to produce adecrypted portfolio file 140 indicating the fund holdings.

The pricing computer 130 receives a price feed 143 periodically (e.g.,every 15 seconds) throughout the trading day that contains currentpricing information at each time t throughout the day. The price feed143 provides pricing information (e.g., bid and ask prices) for a set ofsecurities that preferably includes each security in the fund portfolio.In step 145, the pricing computer computes the value of the decryptedportfolio 140 throughout the trading day for each time t by applyingsome measure of the prices of the securities in the decrypted portfolio140 as received from the quote server 130 at each time t. In step 150,the intra-day value calculated for each time t (“IV_(t)”) is publishedthroughout the trading day, allowing investors to form a basis fornegotiating trading prices of the AMETF shares.

In a preferred embodiment, the portfolio file 115 that is encrypted instep 120 and decrypted in step 135 reflects the fund holdings of theAMETF as of the close of a trading day (including any trading on thatday), and the computing 140 and publicizing 150 steps performed by thepricing computer 130 are performed throughout the next trading day. Inthis embodiment, the pricing computer can use the information from theportfolio file reflecting the holdings of the fund as of the close ofthe previous trading day (including any trading on that day) to estimatethe intra-day value of the current fund holdings on the current tradingday. The portfolio used by the pricing computer to calculate theintra-day value will differ from the actual current AMETF portfolio tothe extent that the fund manager executes trades that change thecomposition of the fund during the current trading day. The intra-dayvalue calculations subsequently performed by the pricing computer thusresult in an intra-day value proxy, because they may be based on aportfolio that does not exactly mirror the fund portfolio. The intra-dayvalue proxy provides sufficient information on which to base the priceof AMETF shares, however, because fund managers do not typically maketrades that change fund composition drastically enough to change fundperformance significantly over the course of a single trading day.Moreover, the NAV calculated at the end of the trading day is based onthe previous day's portfolio.

In an alternative embodiment, the fund computer 110 can update theportfolio file 115 each time a trade is made throughout the trading daythat changes the composition of the AMETF. The updated portfolio filemay be encrypted 120, and sent 127 to the pricing computer 130, whichdecrypts the file 135, and uses the updated information in the decryptedportfolio file 140 reflecting the current fund holdings to calculate theintra-day value 145. This embodiment would eliminate any differencebetween the actual intra-day value and the intra-day value calculatedand published by the PH computer, thus providing the same quantity ofinformation as provided in an embodiment shown in FIG. 2.

The method shown in FIG. 2 can likewise provide the actual currentintra-day value of an AMETF. A portfolio file 115 stored on a fundcomputer 110 can be kept updated throughout the trading day to reflectall trades that affect the composition of the AMETF portfolio. The fundcomputer 110 receives a price feed 143 containing current priceinformation on a set of securities that preferably includes all of thesecurities held in the AMETF. The fund computer calculates the intra-dayvalue of the fund portfolio 115 for each time t (e.g., every 15seconds). The calculated IV_(t) is sent to an exchange computer 200,which may be any computer capable of interfacing with any means forpublishing the IV_(t), such as a stock exchange. In step 220, theexchange computer 200 publishes the IV_(t). Alternatively, the fundcomputer 110 can perform the intra-day value calculation 205 based on aportfolio file 115 that was updated on the previous trading day, but notthroughout the current trading day, to produce an intra-day value proxy.

The methods shown in FIGS. 1 and 2 provide measures of intra-day valuesthroughout the trading day without public disclosure of the underlyingportfolio. But some fund managers may refuse to participate in tradingsystems implementing these methods because they may fear that thecontinuously updated intra-day values or intra-day value proxies canprovide sufficient information for free riders to determine at least themajor fund holdings and front runners to determine fund trading trends.(For example, if the share price of a major holding has a dramatic pricemove that will be reflected in the reported fund value, which will makethe same move). Furthermore, while the intra-day values published bythese methods provide a basis for trading on secondary markets atnegotiated prices, they do not provide additional portfolio informationto market liquidity providers (unless the fund manager is willing toprovide it), making hedging difficult. Thus, the preferred methods ofthe invention described below calculate intra-day value proxies basednot on the fund portfolio from the recent past, but rather on agenerally different portfolio, and these methods can also serve as thebasis for providing a hedging portfolio.

The invention provides systems and methods for constructing a proxyportfolio that may be used to calculate an intra-day value proxy for anAMETF, and that may also be used to construct a hedging portfolio forhedging against trading risks associated with trading in AMETFs withsecret portfolios. These methods involve construction of factor modelsfor AMETFs to construct portfolios that can track the intra-day valuesof the AMETFs and can provide hedging portfolios whose intra-day valuestrack the intra-day values of their AMETFs.

FIG. 3 shows a generalized embodiment of these methods of the invention.

The method depicted in FIG. 3 may be performed on a system involving afund computer 110 and a pricing and hedging computer (“PH computer”)300. The PH computer may be operated by an exchange, a fund company, ora third party. In step 305, the PH computer calculates a set of riskfactors {R_(i)} 310, each of which comprises a historical time series ofdata that reflects a particular risk. Specific embodiments of two typesof risk factor calculations are shown in FIGS. 4 and 5, using aneconomic model and a statistical model, respectively. The risk factors310 are sent to the fund computer 110 in step 315. This sending step andany other step in which data is transferred from one computer to anothermay further involve encryption of the sent data and decryption of theencrypted data, as described above with reference to FIG. 1.

In step 320, the fund computer 110 determines the exposure of the AMETFto the risk factors, to produce a set of fund sensitivity coefficients{{circumflex over (β)}_(i)} 330. Each fund sensitivity coefficient{circumflex over (β)}_(i) measures the exposure of the fund to riskfactor R_(i), that is, how much the value of the fund varies with therisk factor. The step of determining the exposure of the AMETF to riskfactors is further detailed below. In step 325, the fund computer sendsthe fund sensitivity coefficients 330 to the PH computer 300. The PHcomputer can then create a proxy portfolio 335 that has substantiallythe same exposure to the same set of risk factors, and hence hassubstantially the same set of sensitivity coefficients as the fund (orclose to it), but with a generally different set of securities indifferent proportions than those in the actual AMETF portfolio.

In steps 145 and 150, the PH computer can use the proxy portfolio 340 incombination with pricing data for the securities in the proxy portfoliofrom a price feed that is updated periodically (at each time t, forexample, every 15 seconds) throughout the trading day to calculate anIV_(t) in step 145, that is published in step 150. The process ofcalculation of the IV_(t) and publishing the IV_(t) may be repeated foreach updated pricing data received from the price feed throughout thetrading day.

The calculated 145 and published 150 IV_(t) is a proxy for the actualAMETF intra-day value. In this case, however, rather than being based onthe fund asset holdings of the AMETF from the previous trading day (aswas the case in the embodiment described with reference to FIG. 1), theintra-day value proxy is based on a generally completely different setof holdings. This method of calculating the intra-day value based on aproxy portfolio has the benefit of providing an intra-day value thattracks the actual AMETF intra-day value during the day to within anacceptably small difference because both the proxy portfolio and theactual AMETF portfolio are exposed to the same risk factors, and thusbehave very similarly throughout a single trading day. However, it alsoprovides an additional benefit for fund companies, because lessinformation about the AMETF holdings is provided. It is believed to beimpossible to determine an AMETF's holdings from even the fund riskfactor exposure coefficients, let alone from the published intra-dayvalue proxy generated from the proxy portfolio in this method.

The method of FIG. 3 also provides a step 345 for creating a hedgingportfolio 350. Details of how the hedging portfolio may be created areset forth in the descriptions accompanying FIGS. 4 and 5. While in theembodiments shown in FIGS. 3-5 the hedging portfolio is created directlyfrom the fund sensitivity coefficients, alternate embodiments are alsopossible. For example, a hedging portfolio may be created from a proxyportfolio, for example by retaining only the most heavily weightedstocks in the proxy portfolio or performing a risk minimization on theproxy portfolio.

The hedging portfolio can be created from a pre-selected set ofpreferred hedging securities selected, for example, on the basis ofliquidity. It is important for liquidity providers to hedge theirtrading risks with securities that they can easily sell, hence thehedging portfolio may consist of a different set of securities(preferably with more liquidity) than the proxy portfolio. Like theproxy portfolio, however, the hedging portfolio also generally containsa different set of securities in different proportions than the AMETFitself. In one embodiment, the hedging portfolio can be used instead ofthe proxy portfolio to calculate an intra-day value proxy (thuseliminating the need to calculate the proxy portfolio at all). However,it is anticipated that the proxy portfolio would be better suited to thepurpose of intra-day value proxy calculation because there arepreferably fewer limits on the securities that can comprise the proxyportfolio, and hence the intra-day value computed using the proxyportfolio would be expected to more accurately track the actualintra-day value of the AMETF than an intra-day value computed using thehedging portfolio.

FIG. 4 is a specific embodiment of the method depicted generally in FIG.3, and involves an economic factor model. The method of FIG. 4 involvesselection of a group of predetermined economic risk factors 405.Analysis of investment risk through economic risk factors is a wellstudied art, and has produced many different successful pricing models.For example, in the Arbitrage Pricing Theory (APT) economic model,investments are typically analyzed in terms of five basic risk factors:(1) unexpected changes in default premiums, (2) unexpected interest ratechanges, (3) unexpected changes in inflation rates, (4) unexpectedchanges in long term economic growth, and (5) market risk as measured bya benchmark index. See Berry et al., “Sorting Out Risks Using Known APTFactors,” Financial Analysts Journal, March-April 1988, pp. 2941(incorporated entirely herein by reference). Other APT risk factors mayinclude unexpected changes in debt term structure, risk premium, andfirm-specific risks such as firm size effects, leverage, andbook-to-market equity. See, e.g., Fama et al., “Common risk factors inthe returns on stocks and bonds,” J. Financial Economics 33:3-56 (1993);Chan et al. “An Exploratory Investigation of the Firm Size Effect,” J.Financial Economics 14:451-471 (1985); Connor et al., “A Test for theNumber of Factors in an Approximate Factor Model,” J. FinanceXLVIII(4):1263-91 (1993); Rosenberg, “Extra-Market Components ofCovariance in Security Returns,” J. Financial and Quantitative Analysis9:263 (1974); Beckers et al., “The Relative Importance of Common FactorsAcross the European Equity Markets,” J. Banking and Finance 16: 75(1992); Kale et al., “Industry Factors Versus Other Factors in RiskPrediction,” working paper, University of California, Berkeley (1991);and Lehman et al., “The Empirical Foundation of the Arbitrage PricingTheory,” J. Financial Economics 21:213 (1988). (All cited articlesincorporated entirely herein by reference).

Economic risk factor models have been employed to allow investors toevaluate specific risks in their investments. In the present invention,however, an economic risk factor model may be employed to provide amodel for an AMETF portfolio, which may be used to construct proxy andhedging portfolios. This embodiment allows the fund assets to rerhainconfidential, yet provides models for the behavior of those assets thatallow accurate estimation of their intra-day values and creation ofacceptable portfolios for hedging trades of fund shares.

Any set of economic risk factors 405 may be selected to model the AMETFportfolio. Criteria useful for selecting the economic risk factorsinclude measurability (i.e., the risk factors should be based on somemeasurable quantity, such as inflation rates, interest rates, marketindicies, etc.), the availability of historical data on the riskfactors, and the anticipated relevance of the risk factors to the typesof securities expected to be held by the fund to be modeled. In step410, risk factor time series are calculated from historical data. Forexample, risk factor time series may be based on daily, weekly, ormonthly reports of default risks, interest rates, inflation rates,growth projections, and market risks over a period of time such as theprevious year. Other risk factor time series may be based, for example,on more frequent recent reports of prices or returns of securities andcombinations of securities that are sensitive to the selected riskfactors. The time period used for constructing the historical riskfactor time series is preferably recent enough to be relevant to currentcalculations, yet extends in time back far enough that an adequatenumber of reports are incorporated into the time series for robustregression analyses, which are described below.

The risk factor time series 415 of risk factor i is denoted {R_(i,t)}.For a model with five risk factors, for example, i ranges from 1 to 5.The index ‘t’ denotes the historical times at which the risk factor wasreported. For example, if the risk factor time series were to beconstructed from historical data reported daily for the last 20 tradingdays, then t would range from 1 to 20.

In step 420, the PH computer sends the risk factor time series set 415to the fund computer 110. In step 425, the fund computer 110 evaluatesthe exposure of the current AMETF portfolio 115 to the risk factors.This step measures how much each of the risk factors explain theintra-day value of the current AMETF portfolio during the time periodsof the historical data recorded in the risk factor time series. The fundcomputer may access a database of historical pricing data for each ofthe assets in the AMETF portfolio, designated P_(j,t), where P_(j)represents the price of fund security j, and j ranges from 1 to N_(F),the number of securities in the fund. As with the risk factor timeseries, the index t denotes the historical time at which the price wasevaluated. Depending on the construction of the risk factors, the riskexposure calculation 425 may be based on a function of the pricing datafor the AMETF portfolio rather than unmodified historical pricing data.Thus, instead of using pricing data itself, more relevant informationmay be some function of the pricing data F_(j,t), for example, log pricereturns, F_(j,t)=ln(P_(j,t))−ln(P_(j,t-1)), or percentage returns,F_(j,t)=(P_(j,t)−P_(j,t-1))/(P_(j,t-1)), or some other stationaryfunction of the historical pricing data. Whatever function of thepricing data is selected, the same type of function should be used insubsequent calculations.

The risk exposure calculation 425 is a linear regression model thatseeks to explain the past behavior of the AMETF portfolio 115 throughthe past behavior of the selected risk factors. While individualregressions over each security held in the portfolio is one approach, afaster approach uses a single regression for the AMETF as a whole. Atime series of return data for the AMETF can be constructed by summingthe returns for each of the securities currently in the fund:F_(t)=Σ_(j)a_(j)F_(j,t), where a_(j) is the current proportion ofinstrument j to the entire AMETF, and Σ_(j) denotes a sum over theentire range of index j (here, from 1 to N_(F), the number of securitiesin the AMETF portfolio). Sensitivity coefficient estimates {circumflexover (β)}_(i) for the fund can be derived using a linear least squaresregression fit of the following equation:

F _(t)=Σ_(i)β_(i) R _(i,t)+ε_(t),

where ε_(t) denotes the error term, the fund return time series F_(t)and each of the risk factor time series R_(i,t) are known, and theregression fit finds an optimal set of estimated sensitivitycoefficients {circumflex over (β)}_(i). The regression minimizes thevariance

${V(\beta)} = {\frac{1}{N - 1}{\sum\limits_{t}ɛ_{t}^{2}}}$

where N is the number of historical price data points, and is themaximum value of the index τ. The minimization yields an optimal riskfactor vector {circumflex over (β)} with components {circumflex over(β)}_(i). Each of the {circumflex over (β)}_(i) estimates the exposureof the AMETF to risk factor R_(i). Here and in all subsequentlydescribed regressions any other method of extracting the sensitivitycoefficients may be used, but linear least squares regression is fastand has been found to perform well.

The fund computer sends the fund sensitivity coefficient estimates({circumflex over (β)}) 430 to the PH computer in step 432, and the PHcomputer uses them to create proxy and hedging portfolios. In step 440,the PH computer uses the fund sensitivity coefficients to create a proxyportfolio to provide a proxy for the AMETF intra-day value. A databaseof securities that may be selected for inclusion in the proxy portfolio,the proxy universe 435, provides historical pricing data for each of thesecurities in the database. A great deal of variety is possible in theproxy universe, which can include any type of security. The proxyuniverse may contain a greater number of securities than the AMETFitself. If the fund and the risk factors are co-integrated, then pricedata may be used directly; otherwise it may be converted into somefunction of the pricing data such as the log price returnsU_(j,t)=ln(P_(j,t))−ln(P_(j,t-1)) or the percentage returnsU_(j,t)=(P_(j,t)−P_(j,t-1))/(P_(j,t-1)), or some other stationaryfunction of the historical pricing data. To construct the proxyportfolio, a set of weighting coefficients should be determined, whereeach weight w_(j) represents the relative weight of security j in theproxy portfolio. Such weighting could be long or short.

Step 440 can use linear regression to express each of the risk factorsR_(i,t) in terms of linear combinations of the securities in the proxyuniverse using the equation:

R _(i,t)=Σ_(j) w _(i,j) U _(j,t)+ε_(i,t)

where ε_(i,t) is the error term, the returns U_(j,t) are known, and therisk factor time series R_(i,t) are known, leaving the weightingcoefficients w_(i,j) to be determined by regression. Individualregressions can be run for each risk factor R_(i). The regressionsminimize the variance equations

${V\left( w_{i} \right)} = {\frac{1}{N - 1}{\sum\limits_{t}\left( ɛ_{i,t} \right)^{2}}}$

where N is the number of historical data points and w_(i) is the vectorof weighting coefficients that are adjusted during the optimization. Theoptimal weighting coefficients, once determined, provide sufficientinformation to construct the proxy portfolio 445. If the total amount ofmoney invested in the fund to be modeled is M, and P_(j) is the price ofsecurity S_(j) in the proxy universe, then the number of shares ofsecurity S_(j) in the proxy portfolio is given by Mw_(j)/P_(j), wherew_(j)=Σ_(i){circumflex over (β)}_(i)ŵ_(i,j) Accordingly, the proxyportfolio is given by:

${{Proxy}{\mspace{11mu} \;}{Portfolio}} = {\sum\limits_{i}{\sum\limits_{j}\frac{M\; {\hat{\beta}}_{i}{\hat{w}}_{i,j}S_{j}}{P_{j}}}}$

The proxy portfolio can be used as shown in FIG. 3, steps 145 and 150,to calculate and publish an intra-day value proxy for the AMETFthroughout the day.

An identical procedure can be used to create the hedging portfolio instep 450. However, the securities selected for the hedging universe 447may be limited by criteria on the securities that are not required forthe proxy portfolio, which is never traded itself, but rather simplyprovides an intra-day value proxy. For example, the hedging universe 447may be a subset of the proxy universe, where the subset includesactively traded stocks with acceptable risk profiles. In thisembodiment, a linear regression is performed using the known riskfactors and fund sensitivity coefficients, this time to find the weightsof securities in the hedging universe 447 to construct the hedgingportfolio 455. An alternative procedure for constructing hedgingportfolios is described below with reference to the customized hedgingportfolio method of FIG. 6, in which a risk minimizer constructs ahedging portfolio designed to track a proxy portfolio, and selects frominstruments indicated by the liquidity provider who will use the hedgingportfolio.

FIG. 5 is another specific embodiment of the method depicted generallyin FIG. 3, and involves a statistical factor model. Rather than usingpredetermined economic factors, as in the embodiment shown in FIG. 4,the statistical factor model method involves an a priori calculation ofmodel factors based on historical price data from a group of securities.The details of statistical factor models can be found in a number ofreferences. The principal components analysis statistical factor modelwas first described in Pearson, “On Lines and Planes of Closest Fit toSystems of Points in Space,” Philosophical Magazine, 6(2): 559 (1901).Recent applications of principal components analysis can be found inFleurie, “Common Principal Components and Related Multivariate Models”(Wileys, 1988) and Alexander, “Market Models: A Guide to Financial DataAnalysis” (Wileys, 2001). Other relevant references include Feeney,George, and Donald Hester, “Stock Market Indexes: a Principal ComponentAnalysis, Cowles Foundation Monograph” 19, 110-138 (1967); Lessard,Donald R., “International Portfolio Diversification: A MultivariateAnalysis for a Group of Latin Countries,” Journal of Finance 28/3,619-633 (1973); Huberman, Gur, Shmuel Kandel and Robert F. Stambaugh,“Mimicking Portfolios and Exact Arbitrage Pricing,” Journal of Finance42, 1-9 (1987); Connor, Gregory, and Robert A. Korajczyk, “Risk andReturn in an Equilibrium APT-Application of a New Testing Methodology,”Journal of Financial Economics 21, 255-289 (1988); Schneeweiss, Hans andHans Mathes, “Factor Analysis and Principal Components,” Journal ofMultivariate Analysis 55, 105-124 (1995); Chan, Louis K. C, Jason J.Karceski and Josef Lakonishok, “The Risk and Return from Factors,”Journal of Financial and Quantitative Analysis 33/2, 159-188 (1998). Allof the above citations are incorporated entirely herein by reference.

In the embodiment of the invention shown in FIG. 5, a universal tradingdatabase (UTD), comprising a universe of securities 435 from which aproxy portfolio can be constructed, contains historical pricing data foreach of the securities in the proxy universe 435. The proxy universe 435can comprise any number of securities, but preferably contains asufficient number of securities to provide an accurate model for theAMETF portfolio. The number of securities that are sufficient will varydepending on the degree of correlation between the securities in theproxy portfolio and those in the AMETF portfolio. If securities areselected for the proxy universe that are well correlated with thesecurities in the AMETF portfolio, then fewer securities are required inthe proxy universe to accurately model the AMETF.

Step 500 involves a principal components analysis (PCA) of thesecurities in the proxy universe. FIG. 5A provides more detail into thePCA step 500. Historical price data for an instrument i at a past time tis denoted P_(i,t). In step 502, for every instrument i in the proxyuniverse 435, the PH computer can compute a log price return p_(i,t)using Equation 1:

p _(i,t)=ln(P _(i,t))−ln(P _(i,t-1))  (Equation 1)

where P_(i,t) denotes the price of instrument i at time t, and P_(i,t-1)denotes the price of instrument i at the previous fixed interval, timet−1. The price P_(i,t) of, instrument i can be based on the ask price,the bid price, the midpoint price, or any other measure of the price attime t, although the basis for the price is preferably the same forevery instrument in the proxy universe. If the price of instrument iincreased between time t−1 and time t, then the log price return p_(i,t)will be positive, whereas if the price decreased, then the log pricereturn will be negative. While the embodiment discussed here employs logprice returns, many other functions of the time-dependent prices P_(i,t)can be used as discussed above, for example, percentage returns.

The result of step 502 is a set of log return time series p_(i,t) 504.These log return time series are used to construct a correlation matrix,which measures the degree of correlation among the log returns of thevarious instruments in the proxy universe. The correlation matrixelements may be calculated in step 506 using Equation 2:

$\begin{matrix}{c_{ij} = \frac{\left( {\sum\limits_{t}{p_{i,t}p_{j,t}}} \right) - {\left( {\sum\limits_{t}p_{i,t}} \right)\left( {\sum\limits_{t}p_{j,t}} \right)}}{\left. {\left( {{\underset{t}{\left( \sum \right.}\left( p_{i,t} \right)^{2}} - \left( {\sum\limits_{\tau}p_{i,t}} \right)^{2}} \right)\left( {{\sum\limits_{\tau}\left( p_{j,t} \right)^{2}} - \left( {\sum\limits_{\tau}p_{j,t}} \right)^{2}} \right)} \right)^{1/2}}} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

The correlation coefficients c_(i,j) are measures of the degree ofcorrelation between the price fluctuations of instruments i and j, bothin the proxy universe. A high degree of positive correlation betweenprice fluctuations in i and j is observed if their prices rise and fallat the same times by the same amounts, and this is reflected in acorrelation coefficient, c_(i,j), which approaches 1. (Note that if i=j,the correlation coefficient is equal to 1.) Instruments i and j may benegatively correlated: when the price of one rises, the price of theother falls, and vice versa. In this case, the correlation coefficientc_(i,j) approaches −1. If the prices of i and j move independently ofone another, then the correlation coefficient approaches 0. In analternative embodiment, a covariance matrix can be used instead of acorrelation matrix without any substantial changes to the subsequentsteps. If a covariance matrix is used in any step involving a matrix,then covariance matrices are preferably used in all steps involvingmatrices.

The correlation coefficients are real and symmetric, that isc_(i,j)=c_(j,i). The correlation matrix is a real N_(U)×N_(U) squarematrix (where N_(U) is the number of securities in the proxy universe),symmetric about the diagonal, with all the diagonal elements equal to 1.It can be orthogonalized in step 509 to produce a set of eigenvalues andorthogonal eigenvectors. The eigenvalues can be used to eliminate someof the eigenvectors in order to simplify some of the remaining steps ina process detailed in the description of FIG. 5B below. For example, apredetermined number of the smallest eigenvalues (and theircorresponding eigenvectors) can be eliminated, or a more complexelimination method may be used to eliminate all but thoseeigenvalue/eigenvector pairs needed to explain some predeterminedpercent variation in the model.

The principal components of the correlation matrix are computed from theeigenvectors produced in step 509, resulting in orthogonal linearcombinations of the log returns p_(i,t) of all the securities in theproxy universe. The principal components can thus be represented as:

R_(j,t)Σ_(i)w_(i,j)p_(i,t)

where the w_(i,j) are the relative weights of the log return time seriesof instrument i in eigenvector j, and are determined from theorthogonalization of the correlation matrix. These principal componentsare the risk factor time series 510 in this statistical factor model.

The risk factor time series 510 are sent to the fund computer 110, whichdetermines the exposure of the AMETF to the risk factors in step 520. Atime series of return data for the AMETF can be constructed by summingthe returns for each of the securities in the fund portfolio 115:F_(t)=Σ_(j)a_(j)F_(j,t), where a_(j) is the proportion of instrument jto the entire AMETF, and the sum over the index j is from 1 to N_(F)(the number of securities in the AMETF portfolio). Sensitivitycoefficients {circumflex over (β)}_(i) for the fund can be derived usinga linear least squares regression fit of the following equation:

F _(t)=Σ_(i)β_(i) R _(i,t)+ε_(i,t),

where ε_(i,t) is the error term, the fund return time series F_(t) andeach of the risk factor time series R_(i,t) are known, and theregression fit finds an optimal set of sensitivity coefficients β_(i).The regressions minimize the variance

${V(\beta)} = {\frac{1}{N - 1}{\sum\limits_{t}ɛ_{i,t}^{2}}}$

where N is the number of historical price data points, and is themaximum value of the index t. The minimizations yield an optimal riskfactor vector {circumflex over (β)} with components {circumflex over(β)}_(i). Each of the {circumflex over (β)}_(i) estimates the exposureof the AMETF to risk factor R_(i). Any other method of extracting thesensitivity coefficients may be used, but linear least squaresregression is fast and has been found to perform well. The result is afund factor model, in which the fund can be modeled at any time t usingEquation 3:

M_(t)=Σ_(j){circumflex over (β)}_(j)R_(j,t)  (Equation 3)

where R_(j,t)=Σ_(i)w_(i,j)p_(i,t) is based on the log returns p_(i) ofsecurities in the proxy portfolio, the known weights w_(i,j) of theproxy securities i in the risk factor j, and the estimated sensitivityof the fund to risk factor j, {circumflex over (β)}_(j).

The step of determining the exposure of the AMETF to the risk factors inthis statistical factor model is almost identical to the same step inthe economic factor model. The difference is that, generally, the numberof risk factors R_(i) in this statistical model is typically many timesgreater than the number of risk factors in the economic model. Thisgreater number of risk factors provides the benefit of a more detailedand accurate model at the expense of a more complex model and riskfactors with less intuitive meaning. But in both models a simpleregression can provide sensitivity coefficients {circumflex over(β)}_(i), which estimate the exposure of the fund to the risk factors.

Another difference between the economic model and the statistical modelarises in the step of determining the composition of a proxy portfolio.While the economic model performed another regression to calculateweighting coefficients for the securities in the proxy universe thatwould result in substantially the same sensitivity coefficients as theAMETF, the statistical model can instead involve a simple algebraiccombination of the risk factors and find sensitivity coefficients toarrive at a proxy portfolio. The proxy portfolio 445 may be calculatedusing the sensitivity coefficient weighted eigenvectors of thecorrelation matrix. If the total amount of money invested in the fund tobe modeled is M, and P_(j) is the price of security S_(j) in the proxyuniverse, then the number of shares of security S_(j) in the proxyportfolio is given by Mw_(j)/P_(j), where w_(j)=Σ_(i){circumflex over(β)}_(i)w_(i,j). Accordingly, the proxy portfolio is given by:

${{Proxy}{\mspace{11mu} \;}{Portfolio}} = {\sum\limits_{i}{\sum\limits_{j}\frac{M\; {\hat{\beta}}_{i}w_{i,j}S_{j}}{P_{j}}}}$

The proxy portfolio can thus be seen to be a linear combination ofsecurities S_(j), which are members of the proxy universe, with theweight of each security S_(j) in the proxy portfolio given by w_(j). Theproxy portfolio can be used to calculate an intra-day value proxy forthe AMETF, which can be publicized throughout the day, as in theprevious embodiments.

In an alternative embodiment shown in FIG. 5B, the risk model factorsare computed using a multi-stage PCA process 500. As before, a universeof proxy securities 435 is selected from which the proxy portfolio willbe constructed. In this embodiment, however, the securities in the proxyuniverse 435 are initially sorted in step 550 according to somecorrelation, either presumed or calculated. For example, there are oftenwell-recognized correlations between stocks of companies in similarindustrial sectors. Thus one possible, initial sorting would group thesecurities for each distinct industry together. In one embodiment, aninitial culling step can be used to eliminate securities from the proxyuniverse that were not traded enough during the period from which thehistorical pricing data was obtained by setting a predeterminedthreshold trading level, and only keeping those securities that hadtrading activity above that threshold trading level during thehistorical pricing data period.

A preferred embodiment uses the correlation coefficients calculated inEquation 2 to determine which returns of which securities are wellcorrelated, and to group the relatively highly correlated securitiestogether. The securities in each group 555 can be designated now by twoindicies, S_(j,k), which indicates the jth security in the kth group ofsecurities. If N_(k) is the number of securities in group k, then Σ_(k)N_(k)=N_(U) (the number of securities in the proxy universe), where thesum over k is from 1 to N_(g), the number of groups of securities. Theresult of the grouping thus results in a plurality of groupedsecurities, S_(j,k), which are subsets 555 of the proxy universe 435.

Principal components analysis is performed for each subset of securities555 to find the eigenvalues and eigenvectors for each subset.Correlation coefficients are computed according to Equation 2, but onlycorrelations within each subset of securities are computed (i.e., nocross-subset correlations are calculated in this step). Correlationmatrices for each subset are then orthogonalized in step 560, and theeigenvectors and eigenvalues for each subset are determined 562.

In order to simplify subsequent calculations, a number of eigenvectorsmay be eliminated from subsequent calculations by recognizing that theapparent correlation between the returns of two securities in a subsetmay be too small to be a reliable measure of any actual correlation. Instep 563, the N_(k) eigenvalues for each subset k may be organized indecreasing order, starting with the greatest, to form a series λ₁>λ₂> .. . >λ_(Nk-1)>λ_(Nk). Next, some of the smaller eigenvalues can beeliminated according to Equation 4:

λ₁+λ₂+ . . . +λ_(jmax) ≧V*N _(k)  (Equation 4)

where V is a preselected percent variation. To account for, say, 60% ofthe variation in the returns, V would be set to 0.6. The eigenvaluessmaller than λ_(jmax) can be discarded, and their correspondingeigenvectors can also be discarded and need not be used in subsequentcalculations.

Eliminating the smaller eigenvalues provides a simplification of thesubsequent calculations with a minimal effect on the results because theeliminated eigenvalues correspond to eigenvectors that would not beexpected to have an influence on returns correlations above the random“noise” price fluctuations. By first grouping subsets of securities intocorrelated groups, it is expected that most of the eigenvalues (andtheir corresponding eigenvectors) can be eliminated in this culling step563, and thus subsequent calculations using the factors can be vastlysimplified by reducing the dimensionality of the problem for theregression steps. Alternatively, a predetermined number of eigenvectorscorresponding to the largest eigenvalues can be selected, and alleigenvectors with corresponding eigenvalues smaller than the smallesteigenvalue from the predetermined number can be eliminated, or any otheralternative methods for reducing the dimensionality of the subsequentPCA steps may be used.

The PCA 560 and ordering and culling 563 steps results in subsetprincipal components 565 given by f_(j,t)=Σ_(i) w_(i,j)p_(i,t) asbefore, except now the number of principal components is greatly reducedby the culling processes. In this equation for the reduced set ofprincipal components, j ranges from 1 to the number of eigenvectors thatsurvived the culling process across all subsets 555. (Yet each principalcomponent is still a linear combination of all of the securities in theproxy universe.) In order to eliminate any cross-correlations among thereduced set of eigenvectors 565, a second level of principal componentsanalysis is performed in step 570. This time, the PCA analyzescorrelations among all the surviving principal components in the reducedset 565. The correlation matrix elements are given by Equation 5:

$\begin{matrix}{c_{ij} = \frac{\left( {\sum\limits_{t}{f_{i,t}f_{j,t}}} \right) - {\left( {\sum\limits_{t}f_{i,t}} \right)\left( {\sum\limits_{t}f_{j,t}} \right)}}{\left( {\left( {{\sum\limits_{t}\left( f_{i,t} \right)^{2}} - \left( {\sum\limits_{t}f_{i,t}} \right)^{2}} \right)\left( {{\sum\limits_{t}\left( f_{j,t} \right)^{2}} - \left( {\sum\limits_{t}f_{j,t}} \right)^{2}} \right)} \right)^{1/2}}} & \left( {{Equation}\mspace{14mu} 5} \right)\end{matrix}$

and they measure the degree of correlation between principal component iand principal component j. Note that many of these correlation matrixelements will be zero, namely the correlation matrix elements betweenprincipal components from the same subsets, because they involvecorrelation functions between orthogonal principal components resultingfrom a previous correlation matrix orthogonalization.

The eigenvalues from the orthogonalization of the matrix given byEquation 4 can be organized in decreasing order, as before, and many ofthe smaller eigenvalues (and their corresponding eigenvectors) can beeliminated from subsequent calculations. This culling step 572 can bebased on some preselected percent variation, as before, or it can simplybe based on a desire to have no more than a certain number of factors(N) in the subsequent calculations (and thus all of the smallereigenvalues can be eliminated, leaving only the N largest eigenvalues).

The principal components (risk factors) R_(k) of the correlation matrixof Equation 5 are orthogonal linear combinations of the previouslycalculated principal components f_(j,t)=Σ_(i)w_(i,j)p_(i,t):

R_(k,t)=Σ_(j)u_(k,j)f_(j,t)=Σ_(j)Σ_(u)u_(k,j)w_(i,j)p_(i,t)

where k ranges from 1 to N (the total number of factors surviving bothculling steps), and u_(k,j) is a coefficient determined by theorthogonalization of Equation 5 that measures the weight of factor f_(j)in factor R_(k). The risk factor time series can be seen to still belinear combinations of the log returns p_(i), with weightingcoefficients Σ_(j)u_(k,j)w_(i,j). These risk factor time series 510 canbe used as before in step 520 to estimate the fund sensitivitycoefficients {circumflex over (β)}_(k), and in step 540 to produce aproxy portfolio that is a linear combination of the securities S_(i) inthe proxy universe:

${{Proxy}\mspace{14mu} {Portfolio}} = {\sum\limits_{i}\frac{{Mw}_{i}S_{i}}{P_{i}}}$

where each weighting coefficient w_(i)=Σ_(k)Σ_(j){circumflex over(β)}_(k)u_(k,j)w_(i,j) is the proportion of security S_(i) from theproxy universe in the proxy portfolio, M is the total amount invested inthe fund modeled, and P_(i) is the price of security S_(i). This proxyportfolio can be used to calculate an intra-day value proxy for theAMETF, which can be publicized throughout the day as in the previouslydescribed embodiments.

The proxy portfolio may be used in place of the AMETF to derive ahedging portfolio, for example, by running the proxy portfolio through amodel to determine an appropriate hedging portfolio. Alternatively, amethod such as that shown in FIG. 6 may be used to create a hedgingportfolio.

FIG. 6 shows a method that can be used to generate a hedging portfoliofor an AMETF based on a risk factor generated using any of the precedingmethods. This method can use securities from a limited hedging universe600. The securities in the hedging universe can be selected according tocriteria that are desirable in a hedging portfolio, such as liquidityand low risk. In a preferred embodiment, individual liquidity providerswho use the systems of the inventions can specify their own individualhedging universes 600, and individualized hedging portfolios 350 can beconstructed using securities selected from the individual hedginguniverses 600.

Time series of risk factors are constructed according to any method forconstructing time series of risk factors, such as principal componentsanalysis based on log return data, as described above. Preferably, thetime series of risk factors is constructed from securities in a proxyuniverse, which may generally comprise a larger set of securities thanthe hedging universe. The exposure of the AMETF to the risk factors isdetermined, resulting in a set of sensitivity coefficients from which afund factor model M_(t)=Σ_(j){circumflex over (β)}_(j)R_(j,t) can beconstructed in terms of the sensitivity coefficient estimates{circumflex over (β)}_(j) and the factor time series R_(j,t), which arelinear combinations of time series returns of securities in the proxyuniverse.

Step 615 is a calculation for finding a the risk characteristics of eachsecurity in the hedging universe in order to develop a hedging portfoliowith substantially the same sensitivity coefficients to the factors asthe AMETF. This step may involve computing historical return data foreach of the securities in the hedging universe, for example, r_(i,j),which is the log price return for security H_(i) in the hedging universeat time t. Step 615 can be accomplished by the regression analysis ofthe following equation to produce a set of weighting coefficientsŵ_(i,j):

R _(j,t)=Σ_(i) w _(i,j) r _(i,t)+ε_(j,t)

where ε_(j,t) is the error term, and R_(j,t) is risk factor j at time t.The regression minimizes the variance:

${V\left( w_{i,j} \right)} = {\frac{1}{N - 1}{\sum\limits_{t}ɛ_{j,t}^{2}}}$

Each weighting coefficient ŵ_(i,j) measures the exposure of securityH_(i) to risk factor R_(j). The resulting set of hedging universe riskcharacteristics ŵ_(i,j) 620 provides information sufficient to produce ahedging portfolio from the securities in the hedging universe:

${{Hedging}\mspace{14mu} {Portfolio}} = {{\sum\limits_{j}{\sum\limits_{i}{\frac{M}{P_{i}}{\hat{\beta}}_{j}{\hat{w}}_{i,j}H_{i}}}} = {\sum\limits_{i}{\frac{M}{P_{i}}{\hat{w}}_{i}H_{i}}}}$

where each weighting coefficient ŵ_(i)=Σ_(j){circumflex over(β)}_(j)ŵ_(i,j) is the proportion of security H_(i) from the hedginguniverse in the hedging portfolio, M is the total amount invested in thefund modeled, and P_(i) is the price of security H_(i). This hedgingportfolio may be used by liquidity providers and others to hedgeinvestment risks involving the AMETF without providing information aboutthe assets underlying the AMETF, and this portfolio may also be used toprovide an intra-day value proxy for the AMETF. Alternatively, the proxyportfolio may be used to calculate an intra-day value proxy for theAMETF as before.

The set of weighting coefficients ŵ_(i) is not necessarily unique. Thereare potentially many hedging portfolios that can be constructed from thesame hedging universe that all have substantially the same exposure tothe same risk factors as the AMETF and can thus track the AMETF.However, certain sets of weighting coefficients, and hence certainhedging portfolios, may be more desirable than others because they mayprovide substantially the same average returns with less risk, i.e.,less variability of returns. Thus, the hedging portfolio is preferablyoptimized in a subsequent risk minimization step.

A risk minimization procedure, step 640, can be used to improve thehedging portfolio by altering the composition of the hedging portfolioto achieve substantially the same returns as the hedging portfolio withless risk. There are various combinations of assets in a portfolio thatcan give the same expected rate of return. Mean-variance optimization isa technique that adjusts the combination of assets in a portfolio toeither maximize the return for a given level of risk, or minimize therisk for a given level of return (or anything in between). Severalcommercial software packages exist for mean-variance optimization, andthe details of such calculations are known to those skilled in the art.

The risk minimization step 640 requires input in the form of the hedginguniverse risk characteristics 620, historical return data for all of thesecurities comprising the hedging portfolio (i.e., the securities in thehedging universe), a proxy portfolio 645, and historical return datafrom the same period for all of the securities comprising the proxyportfolio. The process calculates the standard deviation of returns foreach security in the hedging portfolio as a measure of the risk for eachsecurity, as well as a correlation matrix of returns between allsecurities in the hedging portfolio.

Based on the risks associated with each of the securities and thecorrelations between the returns of each of the securities, the riskminimization provides a set of portfolios with substantially the sameaverage returns as the proxy portfolio 645 and comprise the samesecurities as the hedging universe 600, weighted by weighting factorsw_(i). An optimized hedging portfolio 650 is selected from the set ofpossible output portfolios expected to achieve substantially the samereturns as the proxy portfolio 645 (and hence also of the AMETF itself),and with the same risk as the proxy portfolio 645, and hence less riskthat the returns of the optimized hedging portfolio 650 will deviatefrom the returns of the AMETF. This optimized hedging portfolio 650 maybe provided to liquidity providers and others who wish to use it tohedge their risks trading AMETF shares. A benefit of this embodiment isthe ability to calculate a hedging portfolio that can accurately trackan AMETF portfolio based on a proxy portfolio, and without requiring anydisclosure of the actual AMETF portfolio.

The various calculations and methods described above can be performed onany computer by any person, limited only by the extent to which the fundcompany wants to keep the AMETF portfolio secret. If disclosure to atrusted third party is acceptable, then many of the calculations can beperformed on the third party computer after certain basic precautionsincluding, for example, encryption of the AMETF portfolio before sendingit to the third party. If disclosure outside of the fund company isunacceptable, than the calculations to determine the exposure of theAMETF to the risk factors should be performed on a computer systeminternal to the fund company. In this embodiment, the fund company (findmanager or fund custodian) may select the parameters for the model.Also, selection of a proxy universe and calculation of the risk factorsin the proxy universe can be done by a computer system internal to thefund company, or by an external computer system. Calculation of ahedging portfolio can likewise be performed on a computer systeminternal or external to the fund company. Furthermore, any or all of thecalculations may be performed on either a single computer, or multiplecomputers, possibly networked together, and thus any computer means maybe used to perform any or all of the calculations.

The invention provides computer software for performing any or all ofthe processes and steps described herein. The computer software may bedivided into component programs for performing the various operationsdescribed herein, operable together across networked computer systems.For example, the software may include a component program for assemblinga proxy universe and calculating risk factors, a separate componentprogram for determining the exposure of an AMETF to risk factors,another component for constructing a proxy portfolio, another componentfor determining an intra-day value proxy, and another component forconstructing a hedging portfolio and an optimized hedging portfolio. Thecomputer software of the invention may be stored on any data storagedevice, including but not limited to, hard drives, floppy disks,CD-ROMs, CD-RWs, DVDs, and solid state storage devices, such as smartmedia.

The invention includes systems for performing PCA calculation processesfor creating intra-day value estimates, proxy portfolios, and hedgingportfolios based on AMETF portfolios. The systems may include softwareprograms for performing the PCA calculations that allow user inputs. Theuser inputs can allow a user to back-test a model of a particular fundto determine the optimal set of parameters for the fund model. A usermay then adjust the user inputs to generate a model with a first set ofparameters, diagnose the model by determining tracking errors andvariances of the model from actual historical fund performance, thenadjust the parameters with the user inputs to improve the model. Theuser inputs may include, for example, the number of principal componentsretained at one or more stages of PCA analysis, the percentage variationto be explained by the principal components retained at one or morestages of PCA analysis, the frequency of historical data to be used ingenerating the model, and the age of the data used in the modeling.Other adjustments may be made to such parameters as the returnsfunctions (e.g., log returns, percent returns, etc.), which may besubject to an exponential or other weighting factor, for example, tofavor more recent historical pricing data over older pricing data, whichmay be less relevant. Other adjustments to calculation parameters mayaffect the size of aggregation buckets, database minimum data densityrequirements, banding time (to reduce spurious data), the number ofreturns used to build the model, the type of weighting (linear,exponential, etc.), the percent variation used for eigenvalue and factorculling, and the total number of factors to be used in the model. Theseuser inputs may be adjusted using dials or slides, for example, in agraphical user interface (GUI).

The invention further includes any sort of financial instrument based onor derived from the AMETFs described herein. The invention thus includesoptions contracts, futures contracts, or any other derivativeinstruments based on the funds of the invention.

While the above description has discussed the application of the systemsand methods of the invention to AMETFs, it will be apparent to thoseskilled in the art that the invention has much broader applicability.Broadly, the invention includes systems and methods for modeling thebehavior of one set of securities using a different set of securities orany other representative indicators. Applications of the inventioninclude, for example, improved security measures for mutual funds.Currently, institutional investors who wish to ensure that their mutualfund's manager is investing in a particular type of securities must hirean independent third party consultant to monitor the fund portfolio. Butdisclosures of fund holdings, even to independent third parties, mayresult in loss of fund secrecy. Using the methods of the invention, afind manager may provide an indicative proxy (or hedging) portfoliocalculated using the systems and methods of the invention, rather thandisclosing the actual mutual fund holdings. Using such an indicativeproxy or hedging portfolio will reduce the likelihood of disclosure ofthe fund assets.

Furthermore, while some of the systems and methods of the inventioninvolve the factor models described above, others may involve differentmathematical techniques to find a set of securities (or otherindicators) to model the performance of a fund. For example, known MonteCarlo methods can be used to select a set of securities to model theperformance of a fund. The invention thus includes any systems ormethods involving any sort of technique for modeling fund performance,where the intra-day value of the model fund substantially tracks theintra-day value of the fund modeled over the course of at least onetrading day.

EXAMPLES Example 1

To test the risk factor model for a variety of portfolios, ninesimulated AMETF portfolios were constructed to represent nine differentapproaches to fund management. Investment securities were selected fromthree groups: small-cap, mid-cap, and large-cap. Within each group,securities were selected to build simulated AMETFs structured forgrowth, value, or a blend. Thus, the nine portfolios consisted of eachof the nine combinations of the three types of securities (growth,value, blend) from the three groups (small-cap, mid-cap, large-cap).Each of the nine portfolios held between 50-100 securities. To simulateactive management, a maximum of a 10% daily turnover of fund holdingswas applied to each of the simulated AMETFs. The intra-day values of thesimulated AMETF portfolios were calculated in 10 minute intervalsthroughout each trading day during the year 2001 based on the historicalprice data from that period.

Nine proxy portfolios were constructed using a principal componentsanalysis as shown in FIGS. 5, 5A, and 5B, based on the simulated AMETFportfolios using historical pricing data from before the time period ofthe simulation. The proxy portfolios were updated on a daily basis toreflect the simulated daily turnover of assets in the simulated AMETFportfolios from the previous day. Intra-day value proxies were computedin 10 minute intervals from the proxy portfolios throughout each tradingday during 2001 based on the historical price data during that period.

The differences between the actual intra-day values of the AMETFs andthe intra-day value proxies were calculated for each 10 minute samplinginterval based on the nine simulated AMETF portfolios and thecorresponding nine proxy portfolios. A statistical analysis was appliedto the value differences. The average value differences and the standarddeviations, as well as the greatest deviations, both positive andnegative, of the intra-day value proxies from the AMETF values (denotedMaximum and Minimum, respectively) are presented below in Table 1.

TABLE 1 Large-Cap Mid-Cap Small-Cap Growth Average −0.019% Average−0.039% Average 0.032% Std. Dev. 0.256% Std. Dev. 0.310% Std. Dev.0.389% Maximum 0.845% Maximum 1.171% Maximum 1.866% Minimum −1.018%Minimum −1.423% Minimum −1.487% Value Average 0.006% Average 0.011%Average 0.010% Std. Dev. 0.201% Std. Dev. 0.216% Std. Dev. 0.307%Maximum 0.878% Maximum 0.915% Maximum 1.371% Minimum −0.943% Minimum−0.727% Minimum −1.242% Blend Average 0.016% Average −0.006% Average0.001% Std. Dev. 0.200% Std. Dev. 0.229% Std. Dev. 0.256% Maximum 1.045%Maximum 1.643% Maximum 1.069% Minimum −0.748% Minimum −0.901% Minimum−1.328%From this table, it is evident that the proxy portfolios produceintra-day value proxies that track the actual intra-day values of theAMETF portfolios with remarkable accuracy. The average differencesbetween the intra-day value proxies and the actual intra-day values foran entire year ranged from just 0.001% (Small-Cap Blend) to −0.039%(Mid-Cap Growth). The standard deviations, which measure the risk thatthe intra-day value proxies will differ from the actual intra-day valuesat any particular time, range from 0.200% (Large-Cap Blend) to 0.389%(Small-Cap Growth). The standard deviations in the difference betweenthe proxy and actual intra-day values shown above would be of anacceptably low risk, and that the proxy intra-day value could serve as areliable basis for negotiating prices of AMETF shares. It is noteworthythat the maximum deviations for an entire year of the intra-day valueproxies from the actual intra-day values are always less than 2% foreach of the nine simulated funds.

Example 2

To demonstrate the accuracy of a risk factor model for a large-cap blendportfolio, a simulated AMETF portfolio was constructed holding between50 and 100 stocks listed in the S&P 500. To simulate active management,a maximum of a 10% daily turnover of fund holdings was applied to thesimulated holdings. The intra-day values of the simulated AMETFportfolio were calculated in 10 minute intervals throughout each tradingday during 2001 based on the historical price data during that period.

A proxy portfolio was constructed using a principal components analysisas shown in FIGS. 5, 5A, and 5B, based on the simulated AMETF portfoliousing historical pricing data from before the time period of thesimulation (the entire 2001 trading year). The proxy universe consistedof the 500 stocks listed in the S&P 500. The proxy portfolio was updatedon a daily basis to reflect the simulated daily turnover of assets inthe simulated AMETF portfolio from the previous day. An intra-day valueproxy was computed in 10 minute intervals from the proxy portfoliothroughout each trading day during 2001 based on the historical pricedata during that period.

A statistical analysis was applied to the intra-day value and intra-dayvalue proxy data generated for the 2001 trading year. The averagedifference between the intra-day value and intra-day value proxy wasonly 0.016%, with an acceptably low standard deviation of only 0.200%. Ahistogram of the results is shown in FIG. 7. These results demonstratethat the returns on the proxy portfolio very accurately tracked thereturns on the simulated AMETF portfolio throughout all of the periodsmeasured. The intra-day value proxy provided an adequate substitute forthe actual intra-day value of the simulated AMETF.

To demonstrate that the proxy portfolio does not give sufficientinformation to infer the actual AMETF portfolio, Table 2 provides acomparison between the top 10 holdings of the simulated AMETF and theproxy portfolio on the same day.

TABLE 2 Top 10 Holdings in AMETF Top 10 Holdings in Proxy PortfolioSymbol Name Weight Symbol Name Weight WPI Watson Pharm. 3.92% CNCConseco Inc. 1.05% TXU TXU Corp. 2.96% APC Anadarko 1.02% Petroleum TGTTarget Corp. 2.81% APA Apache Corp. 0.94% IMNX Immunex Corp. 2.67% SFAScientific-Atlanta 0.85% AHC Amerada Hess 2.53% EOG EOG Resources 0.85%CA Computer 2.37% BR Burlington 0.83% Associates Resources EDS Elec.Data Systems 2.32% RKY Adolf Coors 0.81% ED Consolidated 2.21% VZVerizon Comm. 0.81% Edison PLP Phillips Petroleum 2.21% BUDAnheuser-Busch 0.78% CSX CSX Corp. 2.17% KMG Kerr-McGee 0.76% Total26.16% Total 8.69% Total Number of Holdings 84 Total Number of Holdings474As can be seen from Table 2, there is no overlap between the top 10holdings of the AMETF portfolio and the proxy portfolio in this case.Thus, while the proxy portfolio can accurately track the AMETFportfolio, it does not provide sufficient information to infer the AMETFholdings.

As a further demonstration of the ability of the proxy portfolio totrack the AMETF portfolio throughout the trading day, a proxy portfoliowas constructed from a simulated AMETF and the intra-day value of theproxy portfolio was compared to the intra-day value of the AMETFthroughout the trading day. FIG. 8 shows the results. The averagedifference between the NAV proxy and the actual NAV was only 0.011%,with a very small standard deviation of 0.046%. The top 10 holdings ofthe proxy portfolio and the AMETF portfolio are provided in Table 3.

TABLE 3 Top 10 Holdings in AMETF Top 10 Holdings in Proxy PortfolioSymbol Name Weight Symbol Name Weight RX IMS Health Inc. 2.86% RX IMSHealth Inc. 1.82% MCD McDonald's Corp. 2.68% PVN Providian Financial1.53% NSC Norfolk Southern 2.59% NWL Newell Rubbermaid 1.34% EK EastmanKodak 2.57% CCU Clear Channel 1.15% Comm. GE General Electric 2.48% AVPAvon Products Inc. 1.11% CINF Cincinnati Financial 2.41% GWW WW GraingerInc. 1.08% DVN Devon Energy 2.27% SYY Sysco Corp. 0.97% AGN Allergan2.10% HDI Harley-Davidson 0.97% Inc. CHIR Chiron 2.06% MYG Maytag Corp0.94% BFB Brown-Forman 2.03% MCD McDonald's Corp. 0.93% Total 24.04%Total 11.83% Total Number of Holdings 75 Total Number of Holdings 432

While there are two stocks in common in the top 10 holdings of the AMETFand proxy portfolios (IMS Health and McDonald's), the percentages ofthese stocks held in the two portfolios is very different, and the otherholdings are also different. The information in the proxy portfolio isstill insufficient to infer the holdings of the AMETF, yet asdemonstrated by FIG. 8, the intra-day value tracking is extremelyaccurate.

Example 3

This example demonstrates a method of the invention for constructing ahedging portfolio according to the method shown in FIG. 6, thataccurately tracks an AMETF portfolio using the same set of AMETFportfolio and proxy portfolio used in Example 1. A hedging universe ofsecurities that may be selected for the hedging portfolio was chosenfrom the 80 largest holdings from the proxy portfolio and four exchangetraded funds: SPDR Trust (SPY), MidCap SPDR Trust (MDY), Nasdaq 100Index (QQQ), and the iShares Russell 2000 Index Fund (IWM).

A hedging portfolio was created by applying the fund factor modelcalculated by regression of the AMETF portfolio onto the orthogonalfactors calculated with the PCA methods of FIG. 5. The hedging portfoliowas subjected to risk minimization to provide an optimized hedgingportfolio that tracks the returns given by the proxy portfolio byadjusting the proportions of the securities in the hedging portfolio tominimize the variance of the holdings while maintaining the same averagereturns. An example comparing the top 10 holdings of the hedgingportfolio to the top 10 holdings of the AMETF is provided in Table 4.

TABLE 4 Top 10 Holdings in AMETF Top 10 Holdings in Hedging PortfolioSymbol Name Weight Symbol Name Weight RX IMS Health Inc. 2.86% SPY S&P500 ETF 50.00% MCD McDonald's Corp. 2.68% MDY S&P 400 ETF 27.73% NSCNorfolk Southern 2.59% BR Burlington 3.62% Resources EK Eastman Kodak2.57% AVP Avon Products 2.73% GE General Electric 2.48% EK Eastman Kodak2.13% CINF Cincinnati Financial 2.41% PVN Providian Financial 2.08% DVNDevon Energy 2.27% SEE Sealed Air 2.07% AGN Allergan 2.10% RX IMS HealthInc. 2.05% CHIR Chiron 2.06% SANM Sanmina-Sci 1.97% BFB Brown-Forman2.03% DCN Dana Corp. 1.95% Total 24.04% Total 96.32% Total Number ofHoldings 75 Total Number of Holdings 39The vast majority of the hedging portfolio is comprised of shares of thetwo S&P index funds, which are not AMETF holdings. While there are twostocks in common with the AMETF (IMS Health and Eastman Kodak), theseare held in very different proportions in the hedging portfolio, andthere are no other stocks in common in the top 10 holdings. Furthermore,it is notable that the hedging portfolio contains fewer holdings thanthe AMETF or the proxy portfolio (39 versus 75 or 432), which shouldgreatly reduce transaction costs should the securities underlying thehedging portfolio need to be sold individually.

FIG. 9 provides a demonstration of the accuracy of the hedging portfolioin tracking the intra-day value of the AMETF portfolio (and the proxyportfolio) throughout a trading day. The average difference between theAMETF intra-day value and the hedging portfolio intra-day value was only0.054%, with a standard deviation of only 0.070%. This should be anacceptably small difference and risk for hedging purposes. While theembodiments described above provide illustrations and examples of thesystems and methods of the invention, the invention should not beconsidered at all limited to these embodiments.

1. A method for creating a proxy portfolio for a fund without revealingthe fund assets, comprising the steps of: measuring an exposure of thefund to a set of risk factors to produce a set of fund sensitivitycoefficients, wherein the risk factors comprise a historical time seriesof price data for a set of securities and each fund sensitivitycoefficient indicates the exposure of the fund to one of the riskfactors, storing the fund sensitivity coefficients on computer readablemedia; and using computer means to create a proxy portfolio fromsecurities selected from a proxy universe of securities, wherein theproxy portfolio has substantially the same sensitivity coefficients asthe fund, wherein the proxy portfolio does not reveal the fund assets.2. A method for creating a hedging portfolio for a fund withoutrevealing the fund assets, comprising the steps of: measuring anexposure of the fund to a set of risk factors to produce a set of fundsensitivity coefficients, wherein the risk factors comprise a historicaltime series of price data for a set of securities and each fundsensitivity coefficient indicates the exposure of the fund to one of therisk factors; storing the fund sensitivity coefficients on computerreadable media; using computer means to create a proxy portfolio fromsecurities selected from a proxy universe of securities, wherein theproxy portfolio has substantially the same sensitivity coefficients asthe fund; using computer means to create a hedging portfolio based onthe proxy portfolio, wherein the hedging portfolio does not reveal thefund assets.
 3. A method for creating a reduced risk hedging portfoliofor a fund without revealing the fund assets, comprising the steps of:measuring an exposure of the fund to a plurality of risk factors toproduce a set of fund sensitivity coefficients, wherein the risk factorscomprise a historical time series of price data for a set of securities;storing the fund sensitivity coefficients on computer readable media;using computer means to measure an exposure of each security in a set ofsecurities in a hedging universe to each of the risk factors; and usingcomputer means programmed with risk minimizer software to produce areduced risk hedging portfolio with substantially the same returns andrisk as the fund, wherein the reduced risk hedging portfolio does notreveal the fund assets.
 4. A system for creating a proxy portfolio for afund comprising: computer means programmed to measure an exposure of thefund to a set of risk factors to produce a set of fund sensitivitycoefficients, wherein the risk factors comprise a historical time seriesof price data for a set of securities and each fund sensitivitycoefficient indicates the exposure of the fund to one of the riskfactors, the computer means further programmed to create a proxyportfolio from securities selected from a proxy universe of securities,wherein the proxy portfolio has substantially the same sensitivitycoefficients as the fund and does not reveal the fund assets.
 5. Asystem for creating a hedging portfolio for a fund comprising: computermeans programmed to measure an exposure of the fund to a set of riskfactors to produce a set of fund sensitivity coefficients, wherein therisk factors comprise a historical time series of price data for a setof securities and each fund sensitivity coefficient indicates theexposure of the fund to one of the risk factors; the computer meansfurther programmed to create a proxy portfolio from securities selectedfrom a proxy universe of securities, wherein the proxy portfolio hassubstantially the same sensitivity coefficients as the fund; and thecomputer means further programmed to create a hedging portfolio based onthe proxy portfolio, wherein the hedging portfolio does not reveal thefund assets.
 6. A system for creating a reduced risk hedging portfoliofor a fund comprising: computer means programmed to measure an exposureof the fund to a plurality of risk factors to produce a set of fundsensitivity coefficients, wherein the risk factors comprise a historicaltime series of price data for a set of securities, the computer meansfurther programmed to measure an exposure of each security in a set ofsecurities in a hedging universe to each of the risk factors; and thecomputer means further programmed with risk minimizer software toproduce a reduced risk hedging portfolio with substantially the samereturns and risk as the fund, wherein the reduced risk hedging portfoliodoes not reveal the fund assets.
 7. The system of claim 4, wherein thecomputer is further programmed with a graphical user interface,including a graphical dial, slide bar, or other graphical indicator foradjusting user inputs, wherein the user inputs are selected from thegroup consisting of the size of aggregation buckets, database minimumdata density requirements, banding time, the number of returns used tobuild the model, the type of weighting, the percent variation used foreigenvalue and factor culling, and the total number of factors to beused in the model.
 8. A data storage device storing software to create aproxy portfolio for a fund without revealing the fund assets, thesoftware having instructions for causing computer means to execute thesteps of: measuring an exposure of the fund to a set of risk factors toproduce a set of fund sensitivity coefficients, wherein the risk factorscomprise a historical time series of price data for a set of securitiesand each fund sensitivity coefficient indicates the exposure of the fundto one of the risk factors, creating a proxy portfolio from securitiesselected from a proxy universe of securities, wherein the proxyportfolio has substantially the same sensitivity coefficients as thefund, and wherein the proxy portfolio does not reveal the fund assets.9. A data storage device storing software to create a hedging portfoliofor a fund without revealing the fund assets, the software havinginstructions for causing computer means to execute the steps of:measuring an exposure of the fund to a plurality of risk factors toproduce a set of fund sensitivity coefficients, wherein the risk factorscomprise a historical time series of price data for a set of securities,measuring an exposure of each security in a set of securities in ahedging universe to each of the risk factors; and producing a reducedrisk hedging portfolio with substantially the same returns and risk asthe fund, wherein the reduced risk hedging portfolio does not reveal thefund assets.
 10. A method comprising using computer means to select asecond set of securities that substantially tracks the returns of afirst set of securities over the course of a trading day, wherein thesecond set of securities serves as a proxy for the first set ofsecurities and market participants use the second set of securities toprice the first set of securities without knowing the composition of thefirst set of securities, and wherein the second set of securities doesnot reveal the first set of securities.
 11. The method of claim 10,wherein the computer uses a Monte Carlo method to select the second setof securities.
 12. The method of claim 10, wherein the computer uses arisk factor method to select the second set of securities.
 13. Themethod of claim 12, wherein the risk factor method is an economic riskfactor method.
 14. The method of claim 12, wherein the risk factormethod is a statistical risk factor method.
 15. A method comprisingusing computer means to select a second set of securities thatsubstantially tracks the returns of a first set of securities over thecourse of a trading day, wherein market participants use the second setof securities to hedge a position in the first set of securities withoutknowing the composition of the first set of securities, and wherein thesecond set of securities does not reveal the first set of securities.16. The method of claim 15, wherein the computer uses a Monte Carlomethod to select the second set of securities.
 17. The method of claim15, wherein the computer uses a risk factor method to select the secondset of securities.
 18. The method of claim 17, wherein the risk factormethod is an economic risk factor method.
 19. The method of claim 17,wherein the risk factor method is a statistical risk factor method. 20.The method of claim 15, wherein the second set of securities is ahedging portfolio derived from a proxy portfolio generated by a computermeans to substantially track the returns of the first set of securities.21. An option or derivative instrument based on an exchange traded fundwhose assets are not publicly disclosed on a daily basis, wherein anestimated value of the fund is calculated by: determining a set of riskfactors from a risk factor model; determining a set of fund sensitivitycoefficients and storing the set of fund sensitivity coefficients oncomputer readable media, wherein each fund sensitivity coefficientspecifies the exposure of the fund to one of the risk factors; storingthe fund sensitivity coefficients on computer readable media; usingcomputer means to create a proxy portfolio having substantially the samesensitivity coefficients as the fund; and calculating the estimatedvalue of the fund based on the value of the proxy portfolio, wherein theproxy portfolio does not reveal the fund assets.
 22. A method forcreating a proxy portfolio for a fund without revealing the fund assets,comprising the steps of: measuring an exposure of the fund to a set ofrisk factors to produce a set of fund sensitivity coefficients, whereinthe risk factors comprise a historical time series of price data for aset of securities and each fund sensitivity coefficient indicates theexposure of the fund to one of the risk factors, creating a proxyportfolio from securities selected from a proxy universe of securities,wherein the proxy portfolio has substantially the same sensitivitycoefficients as the fund, and disclosing the proxy portfolio to anentity without knowledge of the fund assets, wherein the proxy portfoliodoes not reveal the fund assets.
 23. A method for creating a hedgingportfolio for a fund without revealing the fund assets, comprising thesteps of: measuring an exposure of the fund to a set of risk factors toproduce a set of fund sensitivity coefficients, wherein the risk factorscomprise a historical time series of price data for a set of securitiesand each fund sensitivity coefficient indicates the exposure of the fundto one of the risk factors; creating a proxy portfolio from securitiesselected from a proxy universe of securities, wherein the proxyportfolio has substantially the same sensitivity coefficients as thefund; creating a hedging portfolio based on the proxy portfolio, anddisclosing the hedging portfolio to an entity without knowledge of thefund assets, wherein the hedging portfolio does not reveal the fundassets.
 24. A method for creating a reduced risk hedging portfolio for afund without revealing the fund assets, comprising the steps of:measuring an exposure of the fund to a plurality of risk factors toproduce a set of fund sensitivity coefficients, wherein the risk factorscomprise a historical time series of price data for a set of securities;measuring an exposure of each security in a set of securities in ahedging universe to each of the risk factors; and generating a reducedrisk hedging portfolio with substantially the same returns and risk asthe fund, and disclosing the reduced risk hedging portfolio to an entitywithout knowledge of the fund assets, wherein the reduced risk hedgingportfolio does not reveal the fund assets.
 25. A method comprisingselecting a second set of securities that substantially tracks thereturns of a first set of securities over the course of a trading day,wherein the second set of securities serves as a proxy for the first setof securities and market participants use the second set of securitiesto price the first set of securities without knowing the composition ofthe first set of securities, and wherein the second set of securitiesdoes not reveal the first set of securities.
 26. The method of claim 25,wherein the step of selecting the second set of securities comprisesusing a risk factor method.
 27. The method of claim 26, wherein the riskfactor method is an economic risk factor method.
 28. The method of claim26, wherein the risk factor method is a statistical risk factor method.29. A method comprising selecting a second set of securities thatsubstantially tracks the returns of a first set of securities over thecourse of a trading day, wherein market participants use the second setof securities to hedge a position in the first set of securities withoutknowing the composition of the first set of securities, and wherein thesecond set of securities does not reveal the first set of securities.30. The method of claim 29, wherein the computer uses a risk factormethod to select the second set of securities.
 31. The method of claim30, wherein the risk factor method is an economic risk factor method.32. The method of claim 30, wherein the risk factor method is astatistical risk factor method.
 33. The method of claim 29, wherein thesecond set of securities is a hedging portfolio derived from a proxyportfolio generated by a computer means to substantially track thereturns of the first set of securities.
 34. A method for determining ahedging portfolio for an actively managed exchange traded fund withoutrevealing the find assets comprising: providing a creation basket forthe actively managed exchange traded fund; determining a set of riskfactors from a risk factor model; determining or receiving a set of fundsensitivity coefficients, wherein each fund sensitivity coefficientspecifies the exposure of the fund to one of the risk factors; andcreating a supplemental portfolio, wherein the hedging portfoliocomprises the sum of the supplemental portfolio and the creation basketof securities, the hedging portfolio has the same sensitivities to theset of risk factors as the fund, and the hedging portfolio does notreveal the find assets.
 35. The method of claim 34, wherein the creationbasket comprises shares of one or more exchange traded funds.